Recursion and Data Structures in Computer Graphics Ray Tracing 1

Forward Ray Tracing  imagine that you take a picture of a room using a camera  exactly what is the camera sensing?  light reflected from the surfaces of objects into the camera lens 2

Forward Ray Tracing 3 light source camera or "eye"

Forward Ray Tracing  forward ray tracing traces the paths of light from the light source to the camera to produce an image  computationally infeasible because almost all of the possible paths of light miss the camera 4

Backward Ray Tracing  backward ray tracing traces the paths of light from the camera out into the environment to produce an image  computationally feasible because the process starts with a single* ray per screen pixel 5

Why Ray Tracing: Shadows 6 shadows with ~1000 light sources Ray Tracing for the Movie 'Cars', P. Christensen et al

Ray Tracing: Reflections 7 Ray Tracing for the Movie 'Cars', P. Christensen et al

Ray Tracing: Reflections 8 Ray Tracing for the Movie 'Cars', P. Christensen et al

Comment on Previous Images  most of the rendering in the previous images was not done using ray tracing  ray tracing was only used on those parts of the image that would produce a noticeable difference 9

Backward Ray Tracing 10

11 Pseudocode for recursive raytracing (missing base cases) Color raytrace(ray) { if ray hits an object { color0 = object_color if object is shiny { color1 = raytrace(reflected_ray) } if object is transparent { color2 = raytrace(transmitted_ray) } return color0 + color1 + color2; } return background_color }

Shadows  we can determine if a point is in shadow by tracing rays from the point to each light source  called shadow rays  if a shadow ray hits an object before it reaches the light source then the point is in shadow 12

Shadows 13 shadowed from L2 shadowed from L3 not shadowed from L1

Reflections  if the ray hits a shiny object then we would like to know what reflection is seen at the hit point  we can cast a new ray in the mirror reflection direction to determine the reflection 14

Reflections 15 incoming rayreflection ray

Transparent Objects  if the ray hits a transparent object then we would like to know what can be seen through the object  we can cast a new ray in the refraction direction to determine what can be seen through the object 16

Transparent Objects 17 incoming ray refraction ray

Recursion  each reflected and refracted ray can be treated as a new view ray emanating from a hit point  i.e., we recursively trace the reflected and refracted rays 18

Ray Tracing as a Binary Tree 19 shadow rays

Stopping the Recursion  what are the base cases?  ray misses all objects  level of recursion exceeds a fixed value  other cases outside the scope of EECS

How Fast is Ray Tracing  approaching real time for non-cinematic quality, e.g.,  Brigade 2 game engine  NVIDA OptiX  demos here if you have a high-end NVIDIA graphics card demos here if you have a high-end NVIDIA graphics card  cinematic quality is much slower 21

How Fast is Ray Tracing  678 million triangles  rays  111 million diffuse  37 million specular  26 million shadow  1.2 billion ray-triangle intersections  106 minutes on 2006 hardware 22

Bounding Volumes  it is easy to compute the intersection of a ray with certain shapes, e.g.,  spheres and cubes  it is hard or expensive to compute the intersection of a ray with arbitrary shapes  idea  put complex shapes inside simple ones 23

Bounding Volumes 24

Hierarchy of Bounding Volumes  why stop at putting complex shapes into bounding volumes?  why not put bounding volumes inside bounding volumes? 25

Hierarchy of Bounding Volumes 26

Spatial Subdivision  instead of putting objects inside volumes we can subdivide space 27

Quadtree Decomposition 28

29 and so on...

Using a Quadtree in Ray Tracing 30

Open Source Ray Tracers  Art of Illusion Art of Illusion  POV-Ray POV-Ray  YafaRay YafaRay  Manta Manta  several others 31